Incremental methods and String-Averaging for non-differentiable convex optimization with inaccurate Subgradients

• Grant number: 15/10171-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: July 01, 2015
• End date: June 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Elias Salomão Helou Neto
• Grantee: Rafael Massambone de Oliveira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

"String averaging" algorithms for the convex feasibility problem, recently shown interesting properties in applications to computerized tomography when generalized appropriately. Until now the theory covers the differentiable convex case restricted to non-negative octant, but non-differentiable functions and more general constraints are of practical interest. This project aims to approach, the theoretical and practical points of view, the convergence of incremental algorithms and "string averaging" under more general conditions, even under the assumption of random error in the computation of subgradients. (AU)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

OLIVEIRA, R. M.; HELOU, E. S.; COSTA, E. F.. String-averaging incremental stochastic subgradient algorithms. OPTIMIZATION METHODS & SOFTWARE, v. 34, n. 3, p. 665-692, MAY 4 2019. (15/10171-2, 13/19380-8, 13/07375-0, 13/16508-3, 17/20934-9)

DE OLIVEIRA, RAFAEL MASSAMBONE; HELOU, ELIAS SALOMAO; COSTA, EDUARDO FONTOURA. String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images. INVERSE PROBLEMS, v. 32, n. 11, NOV 2016. (13/07375-0, 15/10171-2, 13/19380-8, 13/16508-3)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

OLIVEIRA, Rafael Massambone de. String-averaging incremental subgradient methods for constrained convex optimization problems. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.